OSSERMAN LIGHTLIKE HYPERSURFACE CASES

In this study, we constructed four examples of light-like hypersurfaces that satisfy the conditions of an Osserman manifold, based on the characterisation of light-like hypersurfaces of a pseudo-Riemannian manifold of dimension m+2. To this end, we relied on several theoretical results and propositions, particularly those of DUGAL and BEJANCU, in order to establish the conditions under which a light-like hypersurface of a pseudo-Riemannian manifold , can be characterized as an Osserman manifold. This characterization is achieved either through the admissible screen distribution or through the induced algebraic curvature structure. Accordingly, we presented several examples of lightlike hypersurfaces in a semi-Riemannian setting that satisfy the Osserman condition by verifying the required properties of both the Jacobi operator and the induced algebraic curvature.